1. Field of the Invention
The present invention relates to a two-dimensional coding method for holography and more particularly to a two-dimensional coding method for coding binary sequence in correspondence with brightness level of a pixel of a two-dimensional image.
2. Description of the Related Art
In holography technology, signal light and reference light are irradiated to a recording medium, and diffraction grating is formed based on an interference pattern in a recording medium to record a hologram. Then, by irradiating reference light to a recorded hologram, the signal light is reproduced due to diffraction by the hologram. That is, diffracted light from the hologram has the same wave front as the signal light.
The signal light is generated by displaying an image pattern corresponding to digital data, for example, with 0 as a black pixel and 1 as a white pixel, on a spatial light modulator such as a liquid crystal display device and then by intensity-modulating or phase-modulating collimate light. Converting digital data composed of a binary sequence to an image pattern is referred to as two-dimensional coding (Japanese Patent Application Laid-Open (JP-A) No. 9-197947).
Diffracted light from a hologram is detected by a photo detector such as a CCD. A real image of an image pattern is formed on the photo detector. By decoding a binary sequence from this image pattern, digital data is reproduced. If the brightness of the detected pixel (hereinafter referred to as “data pixel”) is equal to or over a threshold value, it is determined to be a white pixel and if it is less than the threshold value, it is determined to be a black pixel.
However, it is difficult to set an absolute threshold value because the intensity of diffracted light is difficult to be maintained at a constant level. Thus, by providing an image pattern with a pixel for reference (hereinafter referred to as “reference pixel”), it is determined whether a pixel is a white pixel or a black pixel from a difference between the brightness of the data pixel and the brightness of reference pixel. The coding method using a difference with respect to the reference pixel is generally called “differential coding method”.
For example, according to a method referred to as a generalized differential coding method, a pixel for reference is provided, and in each of plural pixels in the neighborhood of the pixel for reference, binary data is expressed. For example, 0, 1 of binary data is expressed with black and white pixels respectively. Upon decoding, a difference is calculated between the brightness of the data pixel and the brightness of the reference pixel, and it is determined whether the difference is positive or negative. Whereby, it is determined whether the value corresponds to 0 or 1 of binary data (J. Opt. Soc. Am. A, 12, 2432 (1995)).
Further, according to a method referred to as a gray scale differential coding method, binary data desired to be recorded is expressed with a gray scale in each of plural pixels in the neighborhood of a reference pixel (A) having the lowest brightness and a reference pixel (B) having the highest brightness. Upon decoding, a ratio of a difference in brightness between the data pixel and the reference pixel (B) with respect to a difference in brightness between the reference pixel (A) and reference pixel (B) is calculated. The brightness of the data pixel expressed with the gray scale is detected by multiplying this ratio by the highest tone that can be displayed. Then, binary data is decoded form the brightness value of the data pixel (J. Opt. Soc. Am. A, 12, 2432 (1995)).
However, a conventional differential coding method has various problems. For example, a generalized differential coding method has such a problem that data amount per page is small because it allows expression of 1-bit with a single data pixel. In the gray scale differential coding method, calculation for detecting the brightness of reproduced pixel is complicated, and additional calculation is required for decoding to original binary data using that brightness. Therefore, there is a problem that decoding process is so complicated that reproduction takes a long time.